Phase Retrieval Technique Research Articles

Reference-plane-based fast pixel-by-pixel absolute phase retrieval for height measurement.

Absolute phase retrieval is essential for height measurement in digital fringe projection. However, projections of additional structured patterns that are normally required for phase unwrapping increase the measurement complexity. In this paper, we propose two reference-plane-based pixel-by-pixel absolute phase retrieval techniques with as few projections as possible, suitable for different object depth ranges. The wrapped phase on the object is absolutely unwrapped by referring just to the absolute phase map on the reference plane. Single-frequency absolute phase retrieval with one-reference-plane-based calibration is first proposed for objects within a height limit that equals a calibrated system constant. To extend the measurement depth range, dual-frequency absolute phase retrieval with two parallel reference planes is further proposed. The additional low frequency is used to choose the unwrapping reference from the two reference plane phases for unwrapping the high-frequency phase. Moreover, the proposed techniques are capable of high-frequency absolute phase unwrapping for objects with step-height surface discontinuities. Experiments have been conducted to demonstrate the efficiency of the proposed two techniques.

Multiple color image encryption and authentication based on phase retrieval and partial decryption in quaternion gyrator domain

In this paper, a multiple color image encryption and authentication scheme by using phase retrieval in quaternion gyrator domain and partial decryption is introduced. The quaternion representation is firstly employed to combine three color channels into a single-channel architecture. Then each color image is respectively encoded into a phase-only function according to quaternion gyrator transform based double phase encoding through phase retrieval technique. Subsequently, all phase-only functions are modulated to obtain the final ciphertext. To remain the content of secret images under cover, only a small part of the encrypted data that is selected by multiplying the random binary amplitude mask is preserved for decryption, where nonlinear quaternion correlation is developed to further perform authentication. Since the proposed encryption algorithm is asymmetric, such interest can significantly enhance security of the cryptosystem. The numerical simulations have demonstrated the feasibility and validity of the proposed scheme as well as its better performance compared with other schemes.

A simulation system to hide dynamic objects selectively at visible wavelengths

Currently, invisibility devices are increasingly approaching practical application requirements, such as using easily obtained materials for construction and hiding dynamic objects. Here, using phase retrieval and computer-generated holography techniques, we design an invisibility system in simulation to produce a phase-conjugation signal that changes with the dynamic object to hide it. This system is highly selective for the hidden objects, i.e., it only hides the target object and has no effect on the others. Such function may provide our invisibility system with great potential in special fields, such as biology and military applications for living and dynamic target recognition, selective camouflaging, and others.

A systematic analysis for the quantitative comparison of phase retrieval methods based on alternating projections

We present a numerical and experimental scheme for the systematic analysis and comparison of phase retrieval techniques based on alternating projection numerical methods. This comparison allows us to evaluate the most common and recently introduced phase retrieval methods. The proposed scheme gives a quantitative comparison that helps to elucidate the differences between them and develop proper technical implementations of phase retrieval. The comparison is made by means of a numerical and experimental scheme that allows us to evaluate phase retrieval experiments. In this work, the drawbacks of using arbitrary random initial seeds to support the phase retrieval numerical algorithms are also analyzed and discussed. Moreover, we show the convenience of using a rough object phase estimation, which is obtained by means of a simple holographic technique, as the initial seed. This seed dramatically reduces the computational load of the algorithms by decreasing the successive iterations from hundreds to less than twenty. The experimental object under study is a random phase object within a micro-channel. As a proof of concept, this micro-channel combined with a millimeter size semicircular hole, which provides a reference wave, conforms a primitive sensor. The performance of the algorithms is not only measured by the usual convergence error, but also by means of a quality index that requires a direct comparison against the generally unknown original phase object. Thus, in order to evaluate the experimental performance of the phase retrieval techniques, we implement an interferometric optical setup that allows us to compare the results obtained by both techniques. The experiment proposed is a valuable tool for quantitative experimental evaluation of phase retrieval techniques in the optical domain.

Phase Retrieval for Digital Holographic Microscopy With Defocused Holograms

A new phase retrieval technique in digital holographic microscopy (DHM) with three defocused holograms is proposed. Given the defocusing distance, the phase distributions of tested specimen can be reconstructed with a simple algebraic equation. We have deduced this equation in detail. To avoid the manual operation, the defocused holograms can be flexibly and precisely obtained by introducing an electronically tunable lens based 4f system. This method is suitable for an on-axis hologram as well as the off-axis one but avoids the requirements for not only the iterative process, complex spectrum selection in off-axis DHM or additional phase-shifting devices in on-axis DHM but also the assumption of tested specimen or previous knowledge of the system. A series of simulations and the experimental results of the microlens array and water drop demonstrate the feasibility and effectiveness of the proposed method.

Terahertz ptychography.

We realized a phase retrieval technique using terahertz (THz) radiation as an alternative to THz digital holography, named THz ptychography. Ptychography has been used in x-ray imaging as a groundbreaking improvement of conventional coherent diffraction imaging. Here we show that ptychography can be performed at THz frequencies too. We reconstructed an amplitude and a phase object with both simulated and real data. Lateral resolution accounts to <2λ, while depth variations as low as λ/30 can be assessed.

Relaxation of Alignment Errors and Phase Calibration in Computational Frequency-Diverse Imaging using Phase Retrieval

We demonstrate a computational, frequency-diverse, phaseless imaging technique at microwave frequencies that minimizes the impacts of phase calibration and alignment errors on image reconstruction. Phase calibration error is introduced by means of misaligning the sub-antennas forming an aperture, causing unwanted phase shifts between the forward model and adjoint operation. It is shown that by leveraging phase retrieval techniques, distinguishable images can still be reconstructed in the presence of significant phase errors, while complex-based reconstructions—those relying on measurement of both phase and amplitude—produce heavily corrupted images. Using a frequency-diverse imaging system consisting of a cavity-backed metasurface antenna that operates at microwave frequencies in the K-band (17.5–26.5 GHz), we demonstrate the complex-based and phaseless images of various objects, from a simple subwavelength conducting element to more complex metal structures. We verify that the combination of the phase retrieval approach with the frequency-diverse imager significantly improves the robustness of the composite imaging system to phase errors. While frequency-diverse computational imaging systems have significant advantages in terms of hardware, their reliance on a near-exact forward model places heavy requirements on system calibration. The phase retrieval approach developed here has the potential to alleviate this reliance, increasing the feasibility of such systems.

Extreme ultraviolet holography using a laser-plasma source based on xenon/helium gas puff target

AbstractIn this paper, we present the application of partially spatially coherent extreme ultraviolet (EUV) radiation from xenon plasma from a laser-plasma source, based on a double stream gas puff target, in coherent imaging. The radiation at the wavelength of 13.5 ± 0.5 nm was employed to record Gabor-type holograms. An iterative algorithm, based on a phase retrieval technique, was developed and used to remove the twin image from the reconstructed EUV image of test objects. Using partially coherent radiation from a compact, laser-plasma source based on a double stream gas puff target, which is intrinsically incoherent, a Gabor EUV holography was successfully demonstrated.

In situ antenna diagnostics and characterization system based on RFID and Remotely Piloted Aircrafts

A cost-effective solution for in situ antenna characterization and diagnostics based on Radio Frequency IDentification technology and Remotely Piloted Aircrafts is presented. The cost-effectiveness of the proposed solution is achieved by replacing the radio frequency equipment on-board the small aircrafts with Radio Frequency IDentification tags, while the Antenna Under Test is connected to a Radio Frequency IDentification reader, thus reducing the weight and complexity of the payload of the aircrafts dedicated to antenna measurement task. Received Signal Strength measurements are geo-referred with centimeter-level accuracy thanks to a Real Time Kinematic system. An iterative phase retrieval technique based on the Sources Reconstruction Method is used to recover an equivalent magnetic currents distribution on the Antenna Under Test aperture plane. The reconstructed currents distribution provides antenna diagnostics information and enables the calculation of the antenna radiation pattern. The presented method has been validated by means of measurements in the UHF band for two different antenna arrays with excellent results.

Linear iterative near-field phase retrieval (LIPR) for dual-energy x-ray imaging and material discrimination.

Near-field x-ray refraction (phase) contrast is unavoidable in many lab-based micro-CT imaging systems. Quantitative analysis of x-ray refraction (a.k.a. phase retrieval) is in general an under-constrained problem. Regularizing assumptions may not hold true for interesting samples; popular single-material methods are inappropriate for heterogeneous samples, leading to undesired blurring and/or over-sharpening. In this paper, we constrain and solve the phase-retrieval problem for heterogeneous objects, using the Alvarez-Macovski model for x-ray attenuation. Under this assumption we neglect Rayleigh scattering and pair production, considering only Compton scattering and the photoelectric effect. We formulate and test the resulting method to extract the material properties of density and atomic number from single-distance, dual-energy imaging of both strongly and weakly attenuating multi-material objects with polychromatic x-ray spectra. Simulation and experimental data are used to compare our proposed method with the Paganin single-material phase-retrieval algorithm, and an innovative interpretation of the data-constrained modeling phase-retrieval technique.

A robust multi-image phase retrieval

The phase evaluation is not perfect by using three kinds of existing multi-image phase retrieval methods. The amplitude-phase retrieval scheme is employed for initializing the input of the Multi-stage algorithm to obtain a robust result. The synthesized axial multi-image phase retrieval technique is able to be highly accurate convergent with continuous phase distribution of [0, 2π] and random phase distribution of [0, π], which is also demonstrated to have sharper edge for reconstructed phase map in experiment. This paper will provide a powerful and useful guidance for axial multi-image phase retrieval.

Revising the lower statistical limit of x-ray grating-based phase-contrast computed tomography.

Phase-contrast x-ray computed tomography (PCCT) is currently investigated as an interesting extension of conventional CT, providing high soft-tissue contrast even if examining weakly absorbing specimen. Until now, the potential for dose reduction was thought to be limited compared to attenuation CT, since meaningful phase retrieval fails for scans with very low photon counts when using the conventional phase retrieval method via phase stepping. In this work, we examine the statistical behaviour of the reverse projection method, an alternative phase retrieval approach and compare the results to the conventional phase retrieval technique. We investigate the noise levels in the projections as well as the image quality and quantitative accuracy of the reconstructed tomographic volumes. The results of our study show that this method performs better in a low-dose scenario than the conventional phase retrieval approach, resulting in lower noise levels, enhanced image quality and more accurate quantitative values. Overall, we demonstrate that the lower statistical limit of the phase stepping procedure as proposed by recent literature does not apply to this alternative phase retrieval technique. However, further development is necessary to overcome experimental challenges posed by this method which would enable mainstream or even clinical application of PCCT.

Fourier ptychographic microscopy at telecommunication wavelengths using a femtosecond laser

We report the implementation of the Fourier Ptychographic Microscopy (FPM) technique, a phase retrieval technique, at telecommunication wavelengths using a low-coherence ultrafast pulsed laser source. High quality images, near speckle-free, were obtained with the proposed approach. We demonstrate that FPM can also be used to image periodic features through a silicon wafer.

Phase-step retrieval for tunable phase-shifting algorithms

Phase-shifting (PS) is a well-known technique for phase retrieval in interferometry, with applications in deflectometry and 3D-profiling, which requires a series of intensity measurements with certain phase-steps. Usually the phase-steps are evenly spaced, and its knowledge is crucial for the phase retrieval. In this work we present a method to extract the phase-step between consecutive interferograms. We test the proposed technique with images corrupted by additive noise. The results were compared with other known methods. We also present experimental results showing the performance of the method when spatial filters are applied to the interferograms and the effect that they have on their relative phase-steps.

Coherent laser phase retrieval in the presence of measurement imperfections and incoherent light.

Phase retrieval is a powerful numerical method that can be used to determine the wavefront of laser beams based only on intensity measurements, without the use of expensive, low-resolution specialized wavefront sensors such as Shack-Hartmann sensors. However, phase retrieval techniques generally suffer from poor convergence and fidelity when the input measurements contain electronic or optical noise and/or an incoherent intensity contribution overlapped with the otherwise spatially coherent laser beam. Here, we present an implementation of a modified version of the standard multiple-plane Gerchberg-Saxton algorithm and demonstrate that it is highly successful at extracting the intensity profile and wavefront of the spatially coherent part of the light from various lasers, including tapered laser diodes, at a very high fidelity despite the presence of incoherent light and noise.

Phase problems in optical imaging

Because the phase contains more information about the field compared to the amplitude, measurement of the phase is encountered in many branches of modern science and engineering. Direct measurement of the phase is difficult in the visible regime of the electromagnetic wave. One must employ computational techniques to calculate the phase from the captured intensity. In this paper, we provide a review of our recent work on iterative phase retrieval techniques and their applications in optical imaging.

PR-based SAR reconstruction algorithm for phase noise mitigation based on the hidden convexity

The performance of synthetic aperture radar (SAR) reconstruction is significantly deteriorated by the random phase noises arising from the atmospheric turbulence or frequency jitter of the transmit signal. Recently, the emerging phase retrieval (PR) technique is gradually extended to the SAR reconstruction problem via the phase-corrupted data attributing to its alluring potential for phase noise mitigation. In this paper, a novel PR-based SAR reconstruction algorithm for phase noise mitigation is proposed by jointing alternating direction method of multipliers (ADMM) and Kolmogorov spectral factorization (KoSF). Owing to the exploiting of the hidden convexity of PR-based SAR reconstruction problem and the structure advantage of the quadratic magnitude measurement, the proposed algorithm acquires better robustness for the complex-valued Gaussian white noises and the random phase noises than the existing PR-based SAR reconstruction algorithms. In the experiments, the synthetic scene data and the moving and stationary target recognition Sandia laboratories implementation of cylinders (MSTAR SLICY) target data are provided to verify the validity of the proposed algorithm.

Iterative phase retrieval based on variable wavefront curvature.

An alternative phase retrieval technique is discussed in this paper, which offers some advantages for the obtained resolution and reconstruction procedure. In contrast to commonly applied iterative phase retrieval routines, diffraction patterns with varying distance between the illumination source and the object are recorded. This has the same effect as changing the object sensor distance, albeit offering the advantage of preserving the resolution. Moreover, it is possible to employ the direct Fresnel propagation method without having to worry about different pixel sizes in the reconstruction plane. In addition, the influence of speckle decorrelation has carefully been studied and considered for the experimental implementation.

Generation and Validation of Topological Charges of High-Power Gyrotron Orbital Angular Momentum Beams From Phase Retrieval Algorithm

We present a phase coefficient optimization technique for determining the vortex charge of a high-power orbital angular momentum beam. This high-power vortex beam is generated by transmitting a Gaussian-like beam emitted by a gyrotron with an output power of 25 kW through a spiral phase plate (SPP), which introduces a vorticity at the center of the beam characterized by the geometrical parameters of the SPP. One rigorous, intensity-measurement-based, phase retrieval technique, known as the Gerchberg–Saxton algorithm, does not converge to a correct solution because of the presence of a phase singularity in the high-power vortex beam. Here, we introduce a new phase retrieval algorithm that chooses an appropriate initial phase estimate. This technique yields successful vortex charge determination for both low- and high-power vortex beams. The retrieved intensity profiles show 99.51% and 99.27% intensity regeneration at measurement planes with optimized initial phase estimates for the low- and high-power beams, respectively.

Damage micromechanisms in dual-phase steel investigated with combined phase- and absorption-contrast tomography

The single-distance phase retrieval technique was applied to contrast-enhanced imaging of the dual-phase microstructure of a ferrite/martensite dual-phase with only 1.4% difference in density between the two phases. Each high-resolution absorption-contrast image was registered with a corresponding phase-contrast image, to analyse damage evolution behaviour. The loading step at which each microvoid was nucleated was identified by tracking the microvoid throughout tension, together with its nucleation site. Premature damage initiation was observed at a relatively early stage at various nucleation sites, such as the ferrite interior, martensitic interior and ferrite/martensite interfaces; however, the subsequent growth of such microvoids was relatively moderate. On the other hand, microvoids were also initiated later due to martensitic cracking after the maximum load was reached, and these microvoids subsequently exhibited rapid growth. The martensite cracking induced additional damage evolution mainly along nearby ferrite/martensite interfaces and intersections between the martensite and the ferrite grain boundary. It is notable that the microvoids originating from martensitic cracking exhibited characteristic shear-dominated growth under macroscopic tension, whereas those originating from the other nucleation sites exhibited traditional triaxiality-dominated growth. It was concluded that the ductile fracture was dominated by the substantial force driving the growth of microvoids located on morphologically characteristic martensitic particles.